Compressor Instability with Integral Methods Episode 2 Part 1 docx

Air pressure: p = 0 .5 MPa; abrasive type: Zirconium; abrasive size: dp= 100 μ m abrasive mass flow rate, especially, at the large valve openings.. Thecross-section of the valve opening

Blast Cleaning Equipment

4.1 General Structure of Blast Cleaning Systems

The general structure of a pressure blast cleaning system is illustrated in Fig 4.1 Itbasically consists of two types of equipment: air suppliers and air consumers The

prime air supplier is the compressor At larger sites, storage pressure vessels

ac-company a compressor These vessels serve to store a certain amount of pressurisedair, and to allow an unrestricted delivery of a demanded amount of compressed air

to the consumers The prime air consumer is the blast cleaning nozzle However,

hoses, whether air hoses or abrasive hoses, are air consumers as well – a fact which

is often not considered Another consumer is the breathing air system However,

it is not uncommon to run separate small compressors for breathing air supply; anexample is shown in Fig 4.1 Further parts of a blast cleaning configuration arecontrol devices, valve arrangements and safety equipment

4.2 Air Compressors

4.2.1 General Aspects

Compressed air can be generated by several methods as illustrated in Fig 4.2 Forindustrial applications, the most frequently type used is the screw compressor Screwcompressors are available in two variants: oil-lubricated and oil-free Table 4.1 liststechnical data of screw compressors routinely used for on-site blast cleaning opera-tions Screw compressors feature the following advantages:

r no wear because of the frictionless movements of male and female rotors;

r adjustable internal compression;

r high rotational speeds (up to 15,000/min);

r small dimensions

The fundamental principle for screw compaction was already invented andpatented in 1878 It is based on the opposite rotation of two helical rotors withaligned profiles The two rotors are named as male and female rotors, respectively

C

 Springer 2008

Fig 4.1 Basic parts of a compressed air system for blast cleaning operations (Clemco Inc.,

displacement compressor

Fig 4.2 Compressor types for air compression (Ruppelt, 2003)

Table 4.1 Technical data of mobile screw compressors (Atlas Copco GmbH, Essen)

Nominal volumetric flow rate m 3 /min 21.5 20.4 7.5

The displaced volume per revolution of the male rotor not only depends on eter and length of the rotor but also on its profile One revolution of the main helical

diam-rotor conveys a unit volume q0, and the theoretical flow rate for the compressorreads as follows:

˙

The actual flow rate, however, is lowered by lost volume; the amount of whichdepends on the total cross-section of clearances, air density, compression ratio, pe-ripheral speed of rotor and built-in volume ratio More information is available instandard textbooks (Bendler, 1983; Bloch, 1995; Groth, 1995)

It can be seen in Fig 4.3 that the working line of the compressors and the

working lines of two nozzles intersect The intersection points are called working points of the system This point characterises the parameter combination for the

most effective performance of the system If a compressor type is given, the sitions of the individual working points depend on the nozzle to be used These

po-points are designated “II” for the nozzle “2” with dN= 10 mm and “III” for the

nozzle “3” with dN= 12 mm The horizontal dotted line in Fig 4.3 characterises

the pressure limit for the compressor; and it is at p= 1.3 MPa It can be seen that

volumetric air flow rate in m 3 /min

III II I

Fig 4.3 Working lines of a screw compressor and of three blast cleaning nozzles

the working line of the nozzle “1” with dN = 7 mm does not cross the workingline of the compressor, but it intersects with the dotted line (point “I”) Becausethe cross-section of this nozzle is rather small, it requires a high pressure for thetransport of a given air volumetric flow rate through the cross-section This highpressure cannot be provided by the compressor The dotted line also expresses thevolumetric air flow rate capabilities for the other two nozzles These values can beestimated from the points where working line and dotted line intersect The criticalvolumetric flow rate is ˙QA= 12 m3/min for nozzle “2”, and it is ˙QA= 17 m3/min fornozzle “3” The compressor cannot deliver these high values; its capacity is limited

to ˙QA= 10 m3/min for p = 1.3 MPa, which can be read from the working line of

the compressor However, the calculations help to design a buffer vessel, which candeliver the required volumetric air flow rates

4.2.3 Power Rating

If isentropic compression is assumed (entropy remains constant during the pression), the theoretical power required to lift a given air volume flow rate from a

com-pressure level p1 up to a pressure level p2can be derived from the work done onisentropic compression This power can be calculated as follows (Bendler, 1983):

The ratio p2/ p1 is the ratio between exit pressure ( p2) and inlet pressure ( p1).

These pressures are absolute pressures Results of calculations for a typical sitescrew compressor are displayed in Fig 4.4 It can be seen from the plotted lines thatthe relationship between pressure ratio and power rating has a degressive trend Therelative power consumption is lower at the higher pressure ratios

The theoretical power of the compressor type XAHS 365 in Table 4.1, estimated

with (4.3), has a value of PH= 130 kW In practice, the theoretical power input isjust a part of the actual power, transmitted through the compressor coupling Theactual power should include dynamic flow losses and mechanical losses Therefore,the actual power of a compressor reads as follows:

The mechanical losses, typically amounting to 8–12% (ηKm= 0.08–0.12) of theactual power, refer to viscous or frictional losses due to the bearings, the timing andstep-up gears The dynamic losses typically amount to 10–15% (ηKd= 0.1 − 0.15)

Fig 4.4 Calculated compression power values, based on (4.3)

Table 4.1 is PK = 206 kW If the theoretical power of PH= 130 kW, estimated with(4.3), is related to this value, the losses cover about 36%.

Air compressors can be evaluated based on their specific power consumption,which is defined as the ratio between actual power rating and volumetric air flowrate:

PS= PK˙

For the compressor type XAHS 365 in Table 4.1, the specific power consumption

is, for example, PS= 9.6 kW/(m3/min) Different types of compressors have ent specific power consumptions even if they deliver equal pressure and volumetricair flow rate values Larger compressors have lower specific power consumption;thus, they perform more efficient The physical unit of the specific power consump-tion is that of a specific volumetric energy (kWh/m3), and it can, therefore, alsocharacterise the energy required for the compression of a given air volume.Part of the compression energy is consumed by the heating of the gas Gas tem-perature increases during the compression process For an adiabatic compressionprocess, the final gas temperature can be calculated with the following equation(Bendler, 1983):

( p2 = 0.6 MPa, ϑ1= 20◦C, 60% relative humidity) delivers a condensation water

rate of 8 g per cubic metre of air For a volumetric air flow rate of ˙QA= 10 m3/h, thetotal amount of condensation water would be about 5 l/h Therefore, an after coolingprocess is recommended after the compression process

4.2.4 Economic Aspects

The technical and economical evaluation of compressors is a complex issue

How-ever, the key performance parameters, pressure ( p) and volumetric air flow rate

( ˙QA), usually allow a selection of appropriate consumers (e.g grinders and blast

cleaning nozzles) Key roles in the interaction between compressor and air sumers not only play dimension and condition of the consumers, in particular blastcleaning nozzles (see Fig 4.3); but also the dimensions of connecting devices,

con-Fig 4.5 Calculated air exit temperature after adiabatic compression; based on (4.6)

in particular hose lines, valves and fittings If these parts are insufficiently tuned,efficiency drops and costs increase These aspects are discussed in the followingsections

Pressure losses in hoses, fittings and armatures as well as leakages must also betaken into account if the size of a compressor needs to be estimated This aspect isdiscussed in Sects 4.4 and 4.5

Another problem is pressure fluctuation, which affects the volumetric air flowrate A rule says that even good maintained compressors require a correction factor

of 1.05 This means a plus of +5% to the nominal volumetric flow rate requested bythe consumer

The pressure valve located at the outlet of the compressors should be adjusted

to the nozzle diameter of the blast cleaning system Some relationships are listed

in Table 4.2 A general recommendation is as follows: dVK ≥ 4 · dN For a nozzle

with a diameter of dN= 10 mm, the minimal internal diameter of the compressor

outlet valve should be dVK= 40 mm Values for the sizes of air exit valves of threecompressors are listed in Table 4.1

A good maintenance programme is critical to compressor life and performance

A good maintenance programme is one that identifies the need for service based ontime intervals and equipment hours Additional items that also need to be consideredwhen developing a programme are environmental conditions such as dust, ambienttemperature and humidity, where filter changes may be required before the rec-ommended intervals Most equipment manufacturers have developed a preventive

4.2.5 Aspects of Air Quality

Basically, compressed air can be subdivided into the following four groups:

The requirement for oil-free air comes from surface quality arguments The pancy of blast cleaned steel surfaces by oil will reduce the adhesion of the coatingsystems to the substrate, and it will deteriorate the protective performance Theseaspects are discussed in Sect 8.4 In oil-injected compressors, the air usually picks

occu-up a certain amount of oil due to its way through the compaction room This oil canappear as liquid, aerosol, or even as vapour Even professionally maintained screwcompressors ran without oil separators generate rest oil contents as high as 5 ppm(milligram of oil per cubic metre of air) Part of this oil will be intercepted togetherwith condensation water in appropriate cooling devices However, in order to alsoseparate oil vapour reliably, multiple-step cleaning systems are required A typicalsystem consists of the following components:

r an after-cooler to cool down the compressed air;

r a high-performance fine filter to intercept aerosols;

r an activated carbon filter to absorb oil vapours

Table 4.3 Example of a preventive air compressor maintenance programme (Placke, 2005)

Daily Weekly Monthly Quarterly Bi-yearly Yearly

Compressor oil level C

Radiator cooling level C

Air filter service gauge C

Fuel tank (fill at shift end) C Empty

Water/fuel separator empty C

Discharger of pre-cleaner of air cleaner C

Battery connections/level C

Hoses (oil, air, intake, etc.) C

Automatic shutdown system test C

Air purificator system, visual C

Compressor oil radiator, external C Clean

Engine oil radiator, external C Clean

Scavenging orifice and common elements Clean

Hook Augen bolts Check before towing

Lights (drive, brakes, flasher) Check before towing

Engine oil change, filters, etc Refer to the engine operators manual

A – Change only to the small size unit; B – Change only to the large size unit; C – Check (adjust

or replace as needed); R – Replace; WI – When indicated

Moisture-free compressed air is recommended for blast cleaning operations toavoid moisturisation of abrasive particles Moist particles tend to agglutinate whichcould, in turn, clog pressure air lines Many compressors are equipped with devicesthat remove condensation water These devices include the following parts:

r an after-cooler;

r a condensation water precipitator;

r a filter systems to separate water vapour;

r an air heating systems

There are also anti-icing lubrication agents available that can absorb water andreduce the hazard of ice formation

Max number per m of

particles with given diameter Size inμ m

Content in mg/m 3

Moisture Pressure dew point in◦C

(XW = water in

g/m 3 )

Total oil content

The supply of breathing air is especially important for all blast cleaning tions Critical substances in breathing air include carbon dioxide, carbon monoxide,dust and oil vapour Regulatory limits for breathing air are listed in Table 4.5 Com-pressed air without special treatment cannot meet these requirements Therefore,compressed air needs to be treated in breathing air treatment devices These devicesusually perform in multiple steps, and they include fine filters to intercept water, oiland dust; activated carbon filters to adsorb oil vapour; and catalysts to strip carbondioxide and carbon monoxide

opera-4.3 Blast Machine

4.3.1 Basic Parts

The blast machine is a key part of any dry blast cleaning configuration The majortask of the blast machine is the delivery and dosing of the abrasive particles into theair stream The structure of a typical blast machine is shown in Fig 4.6 It consistsbasically of an air inlet line, a pressure sealing system, the actual storage part and

an abrasive metering system Blast machines are available at numerous sizes

Fig 4.6 Basic design of a blast pot (Clemco, Inc., Washington)

4.3.2 Abrasive Metering

4.3.2.1 Effects of Process Parameters

The metering of the abrasive particles is a challenging task, and the success of ablast cleaning operation depends to some amount on correct and reliable metering(see Sect 6.4.1) The mass flow rate of abrasives is regulated simply due to changes

in the size of the passage in a metering valve Plaster’s, (1972) review still gives

a very good overview on typical pressure vessels and mixing valve designs Morerecent information was provided by Nadkarni and Sharma (1996)

The performance of abrasive metering processes was investigated by Bae et al.(2007), Bothen (2000) and Remmelts (1968) The process of abrasive mass flowmetering due to valve passage size variations is illustrated in Fig 4.7, where theabrasive mass flow rate is plotted against the passage size for a given valve system Apower relationship with a power exponent greater unity can be noted between valveopening size and abrasive mass flow rate The graphs also illustrate the effects ofchanges in nozzle diameter: the larger the nozzle, the more abrasive material waspushed through the valve passage Changes in nozzle diameter seemed to affect the

Fig 4.7 Effects of metering valve passage and nozzle diameter on abrasive mass flow

rate (Remmelts, 1968) Air pressure: p = 0 5 MPa; abrasive type: Zirconium; abrasive size:

dp= 100 μ m

abrasive mass flow rate, especially, at the large valve openings The diameter of theblast cleaning nozzle seemed to influence the power exponents for the individualgraphs The larger the nozzle diameter, the higher was the value for the power expo-nent A critical case is illustrated in Fig 4.7 by the divergent process behaviour forthe largest valve opening – here, a clogging of the abrasive material can be noted Thecross-section of the valve opening was too small to maintain the abrasive deliveryprocess if the abrasive mass flow rate exceeded a value of about ˙mP= 24 kg/min.Therefore, valve size and nozzle diameter must always be adjusted accordingly.Effects of air volume flow rate on the abrasive metering process are shown inFigs 4.8 and 4.9 There is a general trend that abrasive mass flow rate increased ifair volume flow rate increased, but the detailed situation is very complex In the case

of the lower air pressure ( p= 0.4 MPa) in Fig 4.8, the metering process seemed tobecome very unstable at high air volume flow rates It may be considered that thesituation shown in Fig 4.8 applies to micro-blasting processes, which involve verysmall abrasive particles as well as rather small dimensions for the metering device

A precise abrasive metering process could not be maintained under these specialconditions

Abrasive metering is also sensitive to changes in air pressure The higher thepressure, the more abrasive material is pushed through the valve passage (Goldman

et al., 1990; Mellali et al., 1994; Bothen, 2000; Remmelts, 1968) Examples areshown in Figs 4.8 and 4.10 Mellali et al (1994) performed measurements with

0 0

4

8

12

air volume flow rate in l/min

p = 0.4 MPa

p = 0.6 MPa

abrasive size: 82 μm valve passage: 0.63 mm

volumetric air flow rate in l/min

Fig 4.9 Effects of air volumetric flow rate and abrasive particle size on abrasive mass flow rate

for a micro-blasting machine (Bothen, 2000)

as 300% Stallmann et al (1988) measured the abrasive mass flow rate for twoslag materials at three different compressor pressure levels, and they noted rathercomplex relationships as well as abrasive type effects Whereas abrasive mass flowrate increased with an increase in the compressor pressure for copper slag, it showedmaximum values at a moderate compressor pressure for melting chamber slag.Effects of abrasive particle size variations on the performance of abrasive me-tering processes were investigated by Bothen (2000), Goldman et al (1990) andMellali et al (1994) It was shown by Mellali et al (1994) that abrasive mass flowrate delivered by a metering valve arrangement was very sensitive to changes inabrasive particle size Results are provided in Fig 4.10 It can be seen that abrasivemass flow rate increased if smaller abrasive particles were added to the system Thistrend was also found for the use of glass beads by Goldman et al (1990), wherebythe effect of abrasive size seemed, however, to become insignificant at rather low

pressures ( p < 0.2 MPa) For the highest pressure (p = 0.6 MPa) in Fig 4.10, the

difference in abrasive mass flow rate, caused by changes in the abrasive particle size,was as high as 40% Another example for the influence of the abrasive particle size

on abrasive mass flow rate is depicted in Fig 4.9 In that particular case, the abrasivemass flow rate delivered by the metering system was larger for the larger abrasiveparticle diameters at a given valve passage size This result does not agree with theresults delivered by Goldman et al (1990) and Mellali et al (1994) A reason could

be the very small dimensions for the abrasive materials (dP= 23–53μm) and the

valve (dV= 670–1,000μm) used by Bothen (2000)

Adlassing and Jahn (1961) reported on measurements on the effects of abrasivematerial density and abrasive bulk density on the abrasive mass flow rate deliv-ered by an abrasive metering device These authors could prove that the abrasivemass flow rate increased almost linearly with an increase in the abrasive materialdensity The progress of the linear functions was independent of nozzle pressure

( p = 0.2–0.4 MPa) The lowest abrasive mass flow rate was measured for quartzsand (ρP= 2,600 kg/m3;ρB= 1.48 kg/l), and the largest abrasive mass flow ratewas measured for steel cut wire (ρP= 7,900 kg/m3;ρB= 4.29 kg/l)

Figure 4.11 illustrates the effects of nozzle layout and number of valve turns onthe abrasive metering process It can be seen that the geometry of the nozzle affectedthe metering process mainly in the range of high numbers of valve turns However,the general linear trend between number of valve turns and mass ratio abrasive/airdid not seem to be affected by variations in the nozzle geometry Changes in nozzlegeometry have an influence on both air mass flow rate and abrasive mass flow rate

It can be seen that the mass flow ratio abrasive/air took very high values for allnumbers of valve turns; it was basically larger than a value of ˙mP / ˙mA= 2, which

is an upper limit for an efficient blast cleaning process (see Sect 6.4.1) The crease in the mass flow ratio abrasive/air is not only attributed to a larger amount

in-of abrasive flowing through the larger valve opening, but is also due to a reduction

in the volumetric air flow rate This aspect is illustrated in Fig 4.12 The higher thenumber of valve turns, the lower is the volumetric air flow rate measured at the noz-zle Figure 3.11 clarifies the problem from the point of view of abrasive mass flowrate The trends are equal to those shown in Fig 4.12 The geometry of the nozzlehad a pronounced effect on the absolute values for the volumetric air flow rate, but

it did not affect the general trends of the curves If (3.11) and (3.15) are applied,the volumetric air flow rate at the nozzle can be calculated For the conditions inFig 4.12 (assumed air temperatureϑ = 25◦C), the following values were calcu-

lated: nozzle “1” (dN = 11.5 mm): ˙QA= 8.2 m3/min; nozzle “2” (dN= 11 mm):

˙

QA= 7.4 m3/min and nozzle “3” (dN = 12.5 mm): ˙QA= 9.6 m3/min The amount

of displaced air volume depended on number of valve turns, respectively on abrasivemass flow rate; but it could be as high as 50% for the conditions in Fig 4.12 (for ninevalve turns) If, however, the more typical condition of four valve turns is applied,the amount of displaced air volume is between 17% and 25% These values approveresults of measurements performed by other authors (see Sect 3.2.1)

An increase in the number of valve turns increases the abrasive mass flow rate Anincrease in mass flow rate will increase pressure drop in the grit hose, thus reducingthe nozzle pressure This effect is shown in Fig 4.13 It can be seen that the air

Fig 4.11 Effects of number of valve turns and nozzle geometry on the mass flow ratio abrasive/air

in convergent-divergent nozzles (Bae et al., 2007) Nozzle “A” – nozzle length: 125 mm, throat (nozzle) diameter: 12.5 mm, divergent angle: 7.6◦, convergent angle: 3.9◦; Nozzle “D” – nozzle length: 185.7 mm, throat (nozzle) diameter: 9.5 mm, divergent angle: 1.2◦, convergent angle: 8.5◦Nozzle “E” – nozzle length: 215 mm, throat (nozzle) diameter: 11 mm, divergent angle: 1.3◦, con- vergent angle: 7.9◦

pressure at the nozzle dropped if abrasive mass flow rate increased The pressuredrop again depended on the geometry of the nozzle It was most pronounced forthe nozzle “A” For a typical value of ˙mP = 15 kg/min, the air pressure dropped

from p = 0.66 MPa (at the hopper) down to p = 0.53 MPa at the nozzle if a grit hose with a diameter of dH= 32 mm was used (hose length was not given) Thisparticular problem will be discussed in more detail in Sect 4.5.3

The graphs in Fig 4.11 illustrate another permanent problem in abrasive metering.The values for the mass ratio abrasive/air were very high if the number of valve turns

was high Mass ratios of Rm= 1.0–2.0 are most efficient for an effective blast cleaning(see Sect 6.4.1) This optimum range was met for the arrangement in Fig 4.11 for fourvalve turns only Any additional valve turn will deteriorate the blast cleaning processalthough more abrasive mass is being delivered to the cleaning point

4.3.2.2 Metering Models

The aforementioned relationships can be summarised as follows:

˙

mP= f (dV; dN; p; dP;ρ ;ρ ) (4.7)

Fig 4.12 Effects of number of valve turns and nozzle geometry on the volumetric air flow rate

in convergent-divergent nozzles (Bae et al., 2007) Nozzle “1” – nozzle length: 150 mm, throat (nozzle) diameter: 9.5 mm, divergent angle: 2.1◦, convergent angle: 9.3◦; Nozzle “2” – nozzle length: 216 mm, throat (nozzle) diameter: 11.0 mm, divergent angle: 1.3◦, convergent angle: 7.9◦Nozzle “3” – nozzle length: 125 mm, throat (nozzle) diameter: 12.5 mm, divergent angle: 7.6◦, convergent angle: 3.9◦

This complex relationship makes it almost impossible to reliably precalculate acertain desired abrasive mass flow rate

Brauer (1971) reviewed the results of experimental investigations in the field ofbulk material transport, and he suggested the following relationships:

Beverloo et al (1961) developed a model for the approximation of the mass flowrate of particulate solids flowing through the discharge openings of hoppers Themodel considers gravity-induced discharge only, and it is valid for particle sizes

Fig 4.13 Effects of abrasive mass flow rate and nozzle geometry on the nozzle air pressure (Bae

et al., 2007) Nozzle “A” – nozzle length: 150 mm, throat (nozzle) diameter: 11.5 mm, divergent angle: 2.1◦, convergent angle: 9.3◦; Nozzle “C” – nozzle length: 125 mm, throat (nozzle) diameter: 12.5 mm, divergent angle: 7.6◦, convergent angle: 3.9◦; Nozzle “E” – nozzle length: 216 mm, throat (nozzle) diameter: 11.0 mm, divergent angle: 1.3◦, convergent angle: 7.9◦

larger than dP= 500μm Another restriction is dV/dP > 6 The model delivers the

In practice, however, a working characteristic, similar to the graphs shown inFigs 4.7 and 4.11, must be installed for any particular valve type for certain airpressures, nozzle diameters and abrasive materials Such working characteristicsare not available from manufacturers, and it must be estimated experimentally.

4.3.2.3 Abrasive Mass Flow Adjustment

In current industry practice, it is often the potman, who does this adjustment ually How sensitive the entire blast cleaning procedure reacts on such a manualadjustment is illustrated in Fig 6.20 and Table 4.6 Figure 6.20 shows that thecleaning rate was very sensitive to the number of turns for a metering valve Ifthe copper slag was being considered, a change from five turns to six turns led to anincrease in cleaning rate from about 60 m2/h to 72 m2/h (+20%) The results listed

man-in Table 4.6 illustrate the effects of manual fman-ine adjustment on the blast cleanman-ingprocess If the number of turns of the metering valve was changed from 2 to 2.5 forgarnet, cleaning rate almost tripled, and the specific abrasive consumption dropped

up to –30% For the steel grit, the situation was different A change in the number ofvalve turns from 3 to 3.5 did not affect the cleaning rate, but increased the specificabrasive consumption by +30% These examples highlight the economic potential

of a precise abrasive metering

Table 4.6 Metering valve adjustment test data (Hitzrot, 1997)

Abrasive material Number of turns Abrasive mass flow

rate in kg/min

Cleaning rate

in m 2 /h

Specific abrasive consumption

Fig 4.14 Relationship between abrasive mass flow rate, abrasive conveying velocity in an abrasive

hose, and the flow noise (Neelakantan and Green, 1982)

An experienced potman adjusts the abrasive mass flow rate according to the noisedeveloped by the abrasive material if it flows through the hose An optimum flowpattern causes a typical noise (see Sect 4.5.1 for flow pattern types) Results plotted

in Fig 4.14 show that this empirical approach has a physical background The flownoise had distinct relationships with air flow velocity in the hose and abrasive massflow rate These relationships offer the opportunity to control and adjust abrasivemass flow rates by acquiring and treating acoustic signals

4.4 Pressure Air Hose Lines

4.4.1 Materials and Technical Parameters

The transport of the compressed air from the compressor to the blast machine occursthrough pressure lines For on-site applications, these are flexible hose lines Hoselines are actually flexible hoses operationally connected by suitable hose fittings.Hose fittings are component parts or sub-assemblies of a hose line to functionallyconnect hoses with a line system or with each other Pressure air hoses are flexible,tubular semi-finished product designed of one or several layers and inserts Theyconsist of an outer cover (polyamide, nylon), a pressure support (specially treatedhigh-tensile steel wire) and an inner core (POM, polyamide, nylon) Technical pa-rameters are listed in Table 4.7 It can be recognised from the listed values that thehose diameter is an important handling parameter An increase in hose diameter is

Table 4.7 Technical parameters for blast cleaning hoses (Phoenix Fluid Handling Industry GmbH,

4.4.2 Air Hose Diameter Selection

The speed of the air flow through the hose for compressible flow can be calculatedbased on mass flow conservation, which delivers the following relationship:

vF= 4π· mA˙

ρA· d2 H

QA= 10 m3/min, delivered at a pressure of p = 1.0 MPa, the velocity of the air

flow for a hose diameter of dH = 40 mm is vF= 13 m/s More results of calculationsare provided in Fig 4.15

An empirical rule for selecting the proper hose diameter is: the flow velocity inthe hose should not exceed the value ofvF= 15 m/s (Gillessen et al., 1995) Based

on (4.11), the corresponding minimum hose diameter is as follows:

dH= 0.29 · ρ mA˙

A(p, T)

1/2

(4.12)

In that equation, the air mass flow rate is given in kg/s, and the hose diameter is given

in m If no standard diameter is available for the calculated value, the next larger eter should be selected As an example, for an air mass flow rate of ˙mA= 10 kg/min,

diam-delivered at a pressure of p = 1.0 MPa and a temperature of ϑ = 20◦C, (4.12) delivers

a value of dH = 34.5 mm; the recommended internal hose diameter is dH= 38 mm

The critical hose diameters for the situations displayed in Fig 4.15 are: dH= 45 mm

for p = 0.7 MPa; dH= 40 mm for p = 0.9 MPa and dH= 37 mm for p = 1.1 MPa The

lower the pressure, the higher becomes the selected hose diameter The reason is theincrease in volumetric air flow rate if the air pressure drops [see (3.1)] For a given airvolumetric flow rate, the trend between air pressure and critical hose diameter follows

internal hose diameter in mn

limit: 15 m/s

A

50

3 2 1

Fig 4.15 Calculated air flow velocities in blast cleaning air hoses (air flow rate: ˙QA= 10 m 3 /min).

Pressure levels: “1” – p = 0.7 MPa; “2” – p = 0.9 MPa; “3” – p = 1.1 MPa

a power relationship with a negative power exponent (for the examples in Fig 4.15,the power exponent has a value of –0.43)

4.4.3 Pressure Drop in Air Hose Lines

4.4.3.1 General Approach

A permanent problem with air hose lines is the pressure drop in the hose lines Thesituation is illustrated in Fig 4.16 The well-known general approach for estimatingthe pressure drop for incompressible flow is as follows (Bohl, 1989):

1 incompressible flow 2 1 compressible flow 2

is the flow velocity, lHis the hose length, and dHis the hose diameter

However, for compressible flow, which should usually be considered for the airflow in blast cleaning hoses, the pressure drop is not linear, and the air flow velocity

is not at a constant level over the hose length (see Fig 4.16, right drawing) imations for the calculation of pressure losses for compressible flow can be found

Approx-in standard monographs on technical fluid dynamics (Gl¨uck, 1988; Bohl, 1989;Sigloch, 2004) A feasible approximation is as follows (Bohl, 1989):

p2

1− p2 2

ratio between hose diameter and internal wall roughness The general relationship

diameter of dH = 35 mm, the Reynolds number is ReH= 4.1 × 105 More results

of calculations are provided in Fig 4.17 It can be seen that changes in temperaturehave only marginal effects The Reynolds number decreases if the hose diameter

increases A combination of (4.11) and (4.18) delivers the relationship: ReH∝ d−1

H The precise solution to (4.17) is a function of the flow type in the hose and thethickness of the laminar boundary layer at the hose wall For blast cleaning pro-

cesses, a turbulent flow (ReH > 2,300) is basically assumed However, even if the

flow is turbulent, a thin laminar boundary layer forms at the wall regions of thehoses (Bohl, 1989; Wille, 2005) This laminar layer is illustrated in Fig 4.18 Thethickness of this layer can be calculated as follows (Wille, 2005):

Results of (4.19) are displayed in Fig 4.19 It can be seen that air temperaturedoes not have a notable effect on the thickness of the boundary layer But the ef-fect of the hose diameter is very pronounced Combining (4.11), (4.18) and (4.19)delivers the relationship:δH∝ d3/2

H

the so-called Blasius equation can be utilised to calculate the friction number for a

Reynolds number range between ReH= 2.3 × 103and 105(Bohl, 1989):

Fig 4.17 Calculated Reynolds numbers for the flow of air in blast cleaning air hoses for two values

of air temperature (air volume flow rate: ˙QA= 10 m 3/min, air pressure: p= 1.0 MPa)

Fig 4.18 Structure and parameters of a laminar boundary layer on a hose wall (Wagner, 1990)

Fig 4.19 Calculated values for the thickness of laminar boundary layers for the flow of air in blast

cleaning hoses for two values of air temperature

In these cases, the friction number is independent of the wall roughness, and it is

a function of the Reynolds number only Equations (4.20) and (4.21) are graphicallyexpressed in Figs 4.20 and 4.21 Typical values forλAcan be read from these twographs

the friction number can be estimated from the so-called Prandtl–Colebrook charts,which can be found in standard books on technical fluid mechanics (Oertel, 2001;Wille, 2005) A Prandtl–Colebrook chart is displayed in Fig 4.22 If the Reynolds

number and the ratio dH/kHare known, the corresponding value forλAcan be read at

the ordinate The special case hydraulically smooth is also included in that graph A

general empirical relationship for the turbulent flow regime is the Colebrook-Whiteequation (Wille, 2005):

men-Fig 4.20 Friction parameter for hydraulically smooth flow conditions at high Reynolds numbers:

Blasius’ solution (4.20)

Fig 4.21 Friction parameter for hydraulically smooth flow conditions at very high Reynolds

num-bers: Nikuradse’s solution (4.21)

Fig 4.22 Relationships between Reynolds number, relative roughness and friction parameter

(Wille, 2005) 1-hydraulically smooth; 2-hydraulically rough (limit)

kH = 0.016 mm (Bohl, 1989) This value is one order of magnitude lower thanthe typical values for the thickness of the laminar boundary layer (see Fig 4.19).The Reynolds numbers for the flow in blast cleaning hoses usually exceed the value

ReH= 105(see Fig 4.17) Therefore, the rather simple (4.21) can be applied for theestimation of the friction number for most blast cleaning applications

4.4.3.3 Hose Diameter Effects

The equations mentioned above deliver the following relationship between pressuredrop and hose diameter:

⌬pA∝ d−5

This equation illuminates the overwhelming influence of the hose diameter on thepressure loss (A precise physical deviation delivers a power exponent value some-what smaller than 5.) This influence is graphically expressed in Fig 4.23, whichshows results of measurements of the pressure drop in hoses with different diame-

ters The rapid pressure drop in the hose with the small diameter of dH= 19 mm can

be recognised These experimental results agree very well with results calculatedfrom (4.14) More values, calculated with (4.14), are plotted in Fig 4.24 The graphsshow, among others, that pressure drop reduces at higher air pressures This phe-nomenon can be explained with (3.6), which suggests that the air density increaseswith an increase in pressure Higher air density means lower air volume, which inturn reduces the air flow velocity in the hose Equation 4.14 shows that lower air flowvelocity leads to less pressure drop More relationships are displayed in Fig 4.16.The graphs show the relationship between hose length and air flow velocity in the